Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:

import java.util.HashSet;
import java.util.Scanner;

public class A {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        HashSet<Long> H = new HashSet<Long>();
        for (long i = 1; (i * (i + 1)) < 2 * n; i++) {
            H.add((i * (i + 1)) / 2);
            if (H.contains(n - (i * (i + 1)) / 2)) {
                System.out.println("YES");
                return;
            }
        }
        System.out.println("NO");
    }
}